This paper begins by tracing interest in emergence in physics to the work of condensed matter physicist Philip Anderson. It provides a selective introduction to contemporary philosophical approaches to emergence. It surveys two exciting areas of current work that give good reason to re-evaluate our views about emergence in physics. One area focuses on physical systems wherein fundamental theories appear to break down. The other area is the quantum-to-classical transition, where some have claimed that a complete explanation of the behaviors (...) and features of the objects of classical physics entirely in quantum terms is now within our grasp. We suggest that the most useful way to approach the emergent/non-emergent distinction is in epistemic terms, and more specifically that the failure of reductive explanation is constitutive of emergence in physics. (shrink)
One important aspect of biological explanation is detailed causal modeling of particular phenomena in limited experimental background conditions. Recognising this allows one to appreciate that a sufficient condition for a reduction in biology is a molecular model of (1) only the demonstrated causal parameters of a biological model and (2) only within a replicable experimental background. These identities—which are ubiquitous in biology and form the basis of ruthless reductions (Bickle, Philosophy and neuroscience: a ruthlessly reductive account, 2003)—are criticised as merely (...) “local” (Sullivan, Synthese 167:511–539, 2009) or “fragmentary” (Schaffner, Synthese, 151(3):377–402, 2006). However, in an instructive case, a biological model is preserved in molecular terms, demonstrating a complex phenomenon that has been successfully reduced. (shrink)
One important aspect of biological explanation is detailed causal modeling of particular phenomena in limited experimental background conditions. Recognising this allows a new avenue for intertheoretic reduction to be seen. Reductions in biology are possible, when one fully recognises that a sufficient condition for a reduction in biology is a molecular model of 1) only the demonstrated causal parameters of a biological model and 2) only within a replicable experimental background. These intertheoretic identifications –which are ubiquitous in biology and form (...) the basis of ruthless reductions (Bickle 2003)- are criticised as merely “local” (Sullivan 2009) or “fragmentary” (Schaffner 2006). However, in an instructive case, a biological model is preserved in molecular terms, and a complex biological phenomenon has been successfully reduced. In doing this the molecular model remains valid in a broader range of background conditions and meaningfully unites disparate biological phenomena. (shrink)
Our objective was to explore the relationships between adult attachment and various aspects of emotional awareness, including alexithymia and level of emotional awareness. Participants were 112 university students who completed the Attachment Style Questionnaire, the Bermond-Vorst Alexithymia Questionnaire (BVAQ), and the Level of Emotional Awareness Scale. We found that alexithymia was positively related to the avoidant attachment style and negatively with the anxious attachment style. Anxious style-but not avoidance-was also related to the level of emotional awareness. An analysis of the (...) four attachment categories revealed subtle differences regarding the subscales of the BVAQ. Findings are discussed with reference to internal working models of self and others, highlighting the relationship between emotional awareness impairment and interpersonal behaviour. Keywords: alexithymia; emotional awareness; attachment; internal working model; BVAQ; LEAS (Published: 7 March 2012) Citation: Socioaffective Neuroscience & Psychology 2012, 2 : 10744 - DOI: 10.3402/snp.v2i0.10744. (shrink)
A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness and (...) completeness -- Why is first order logic "First Order"? (shrink)
Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism W. (...) Hugh Woodin; 6. Concept calculus: much better than Harvey M. Friedman; Part IV. Perspectives on Infinity from Physics and Cosmology: 7. Some considerations on infinity in physics Carlo Rovelli; 8. Cosmological intimations of infinity Anthony Aguirre; 9. Infinity and the nostalgia of the stars Marco Bersanelli; 10. Infinities in cosmology Michael Heller; Part V. Perspectives on Infinity from Philosophy and Theology: 11. God and infinity: directions for future research Graham Oppy; 12. Notes on the concept of the infinite in the history of Western metaphysics David Bentley Hart; 13. God and infinity: theological insights from Cantor's mathematics Robert J. Russell; 14. A partially skeptical response to Hart and Russell Denys A. Turner. (shrink)
Robin Horton has studied modes of thought for decades. His attitude is strongly "intellectualist" and directed against "symbolic" interpretation in anthropology A contrast between these two standpoints is regarded in this paper as axiomatic, derived from worldview assumptions presented as a scientific debate. Divergences concern isssues such as the objective status of human cognition, the degree of rationality of a given thought system, and the desirable status of anthropological interpretations of human thought. Horton's standpoint is criticized, mainly his views on (...) the universality of standards of rationality established in the West, and the presentism of his "cognitive foundationalism," which claims that cognition is the primary function of any thought/belief system. His intellectualist position is placed in the context of contemporary postmodern anthropological discourses. (shrink)
Extending the ideas from (Hofer-Szabó and Rédei [2006]), we introduce the notion of causal up-to-n-closedness of probability spaces. A probability space is said to be causally up-to-n-closed with respect to a relation of independence R_ind iff for any pair of correlated events belonging to R_ind the space provides a common cause or a common cause system of size at most n. We prove that a finite classical probability space is causally up-to-3-closed w.r.t. the relation of logical independence iff its probability (...) measure is constant on the set of atoms of non-0 probability. (The latter condition is a weakening of the notion of measure uniformity.) Other independence relations are also considered. (shrink)
Abstract The first fractal constructions appeared in mathematics in the second half of the 19th century. Their history is divided into two periods. The first period lasted 100 years and is a good example of the method of proofs and refutations discovered by Lakatos. The modern history of these objects started 20 years ago, when Mandelbrot decided to create fractal geometry, a general theory concentrated on specific properties of fractals. His approach has been surprisingly effective. The aim of this paper (...) is to examine the reasons for Mandelbrot's success and for the present popularity of fractals. They are now known not only in mathematics but also in many fields of natural, social and applied sciences, and even in the arts. (shrink)
We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give (...) its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones. (shrink)
We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus ( DFL ) whose algebraic semantics is the class of distributive residuated lattices ( DRL ). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1].
In this paper we give a positive answer to a problem posed by G. Hofer-Szabo and M. Redei (2004) regarding the existence of infinite common cause systems (CCSs). An example of a countably infinite CCS is presented, as well as the proof that no CCSs of greater cardinality exist.
We introduce a three-tiered framework for modelling and reasoning about agents who (i) can use possibly complete reasoning systems without any restrictions but who nevertheless are (ii) bounded in the sense that they never reach infinitely many results and, finally, who (iii) perform their reasoning in time. This last aspect does not concern so much the time it takes for agents to actually carry out their reasoning, as the time which can bring about external changes in the agents’ states such (...) as arriving of new information or discarding previously available information due to bounds of the agent’s resources. These three aspects are treated with the maximal possible degree of independence from each other. The treatment of layer (iii) can be combined with arbitrary logic at level (ii) which, in turn, can be combined with arbitrary agent logic at level (i). At the level (iii), we discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until’ or ‘chop’ operator), and is interpreted over dense linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about single states). We give the main idea of the completeness proof and suggest a wide range of possible applications, which is a simple consequence of the parametric character of both the language and the reasoning system. We address then in more detail the case of non-omniscient rational agents, (ii). Their models are syntactic structures (sets of available formulae) similar in spirit, though not in the technical formulation, to the models used in other syntax oriented approaches and in active logic. We give a new sound, complete and decidable system for reasoning about such agents. Finally, we illustrate its extensions with the internal reasoning of agents, (i), by equipping them with some example logics. (shrink)
I present a fragment from thehistory of the Russian reception of HerbertSpencer''s sociology. The discussion concernstwo diametrically opposed but exceptionallyimportant figures in the history of Russianthought, Nikolai Mikhajlovskij (1842–1904) andKonstantin Leont''ev (1831–1891). As one of thechief ideologues of the Populist movementMikhajlovskij turned Spencer''s ideas into anegative frame of reference for his own`romantic socialist utopia''. In turn, Leont''evformulated his extremely conservative politicalviews on the basis of Spencer''s organicistsociology. Though at the opposite ends of thespectrum both standpoints succeeded inexhibiting the political implications (...) of thepositivist and naturalist style of thinking. (shrink)
In this paper we study the status of the arithmetical completeness of dynamic logic. We prove that for finitistic proof systems for dynamic logic results beyond arithmetical completeness are very unlikely. The role of the set of natural numbers is carefully analyzed.
We applaud the authors' basic message. We note that the negative research emphasis is not special solely to social psychology and judgment and decision-making. We argue that the proposed integration of null hypothesis significance testing (NHST) and Bayesian analysis is promising but will ultimately succeed only if more attention is paid to proper experimental design and implementation.
We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is (...) continuous in model class topology). (shrink)
Quality is usually considered to be an attribute of an object, its degree of excellence or, more subjectively, fitness for use. Stemming from this point of view, the goal of most ranking systems is to find efficient ways of discovering, or rather uncovering, the quality of specific products or services. However, from a social psychological perspective it seems that the notion of quality belongs predominantly to the realm of social relationships. We argue that quality exists mainly between the users of (...) an object, not within the object itself, and its functions are predominantly social, i.e. promoting interactions, creating a shared reality, or building social relationships. Quality is constructed in social interactions and used as a token therein. In the present paper we outline the social functions of quality, and discuss the implications of this perspective for designing more useful recommendation systems. (shrink)
At Protagoras 353de, Socrates gives three possible reasons for calling some pleasures `wrong'. Scholarly attention has focused on the second of these, according to which pleasures are `wrong' when they have negative consequences. This paper argues that the first reason (the pleasures are fleeting) corresponds to beliefs held by Democritus, among others; and that the third reason (the pleasant things “give pleasure in whatever way and for whatever reason“) is the view adopted by Socrates in the dialogue.
Over the past 20 years the Polish town of Owicim, the site of the most infamous death camp, has seen a series of well-publicised disputes over land use around the Auschwitz Museum. Each of these disputes has featured certain groups making certain claims for the 'appropriate' use of land. The public's perception outside Poland of these disputes has been guided by Jewish groups prioritising their claims above all others. There has been a failure to recognise how far Polish claims are (...) rooted in other equally valid moral geographies, not least those shaped both by Polish Catholic and communist traditions. (shrink)
The theorem to the effect that the languageL introduced in [2] is mutually interpretable with the first order language is proved. This yields several model-theoretical results concerningL.
In a recent paper, Cavusoglu and Tebaldi (2006) provided an evaluation of neoclassical and endogenous growth theories according to Lakatos's methodology of scientific research programmes. This paper offers three criticisms of their contribution as well as a rival Lakatosian appraisal of growth theories. First, we hold that Cavusoglu and Tebaldi do not provide a proper structure of theory comparison in their contribution. Second, we argue that they use an inadequate version of Lakatos's appraisal criterion. Third, against the claim (...) of the authors, we show that there are seminal endogenous growth models, which predict income convergence among countries. Finally, in contrast to Cavusoglu and Tebaldi, our analysis suggests that by Lakatos's standards, Schumpeterian variant of endogenous growth theory is both theoretically and empirically progressive over neoclassical growth theory. (shrink)
The following paper discusses John of St. Thomas’ study of the way in which a habit (moral or epistemic virtue or vice) is a cause of an action it prompts. I begin with contrasting the question of causality of habits with the general question of the causal relevance of dispositions (2). I argue that habits constitute a very peculiar kind of dispositions marked by the connection with the properties of being difficult and being easy, and there are some special reasons (...) to admit the irreducibility of dispositions of this kind. I argue also that there is a special sort of causal connection between a habit and an action it actually prompts. Then I present an analysis of four theses of John of St. Thomas on the causality of habits, which, I think, constitute the most mature and reliable study of the causality of habits in the scholastic tradition: (i) Habits are efficient causes of actions they prompt (3.1). (ii) Virtues do determine the very natures of actions they prompt (3.2); (iii) Virtues do not have a proper counterpart among the characteristics of actions they prompt (3.3); (iv) The formal object of causality of virtue is a masterpiece performance of an action (3.4). In my analyses of John’s arguments for these theses I make three claims: not all powers are “in state of readiness for action”; habits are powers of powers or dispositions of powers; the general concept of a strategy is the key to grasp the properties of being difficult and being easy, and habits should be analysed as a kind of strategies. (shrink)
The first task of the philosophy of nature -- The problem of elementarity -- The philosophical myth of creation : the Platonic philosophy of nature -- Aristotle's Physics -- Aristotle's method of cosmological speculation -- Descartes' mechanism -- Isaac Newton and the mathematical principles of natural philosophy -- The world of Leibniz : the best of all possible worlds -- Immanuel Kant : the a priori conditions of the sciences -- The romantic philosophy of nature -- The cosmology of Whitehead: (...) the universe as process -- Popper's open universe -- Science as philosophy -- Problems and methods of the philosophy of nature. (shrink)
A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)
Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.
We introduce a nonstandard arithmetic $NQA^-$ based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by $NQA^+$ ), with a weakened external open minimization schema. A finitary consistency proof for $NQA^-$ formalizable in PRA is presented. We also show interesting facts about the strength of the theories $NQA^-$ and $NQA^+$ ; $NQA^-$ is mutually interpretable with $I\Delta_0 + EXP$ , and on the other hand, $NQA^+$ interprets the theories IΣ1 and $WKL_0$.
Cognitio abstractiva secundum Scotum: elementa doctrinaeSecundum Duns Scoti sententiam cognitio abstractiva est, quae ab actuali existentia obiecti non dependet, et ideo speciebus impressis niti debet. Scotus nonnulla argumenta pro necessitate speciei intelligibilis ad cognitionem abstractivam universalem perficiendam praebet. Reiectis sententiis eorum, qui causam cognitionis aut obiectumsolum, aut intellectum esse putabant, Scotus causam totalem cognitionis ex obiecto cognito et intellectu ut ex causis partialibus essentialiter ordinatis componi concludit: species intelligibilis et a phantasmate, et ab intellectu agente causatur. Hoc modo ovus repraesentationis (...) ordo oritur, in quo natura communis in modo universalitatis repraesentetur. Processus cognoscendi a Scoto ut successio dynamica actionum et passionum describitur. Ex dictis patet, Scoti de cognitione doctrinam a traditione Aristotelica discedere et germina epistemologiae modernae continere elucet.Abstractive cognition according to Duns Scotus: the Basic ApproachAccording to Scotus, abstractive cognition is independent of the actual existence of its object, and must therefore rely on the intentional species. Scotus presents several arguments in favour of the necessity of the species intelligibilis for abstractive universal cognition. After discussing opinions that ascribed exclusive causality in the process of cognition either to the intellect or to the object, Scotus arrives at the conclusion that both the object and the intellect act as essentially ordered partial causes of cognition: the intelligible species is caused both by the phantasm and the active intellect. Thus results a new order of representation, in which the common nature is represented as universal. The process of cognition is described by Scotus as a dynamic succession of active and passive phases. On the basis of these and other characteristic features, Scotus’s epistemology can be described as departing from the Aristotelian tradition, and as the locus of the first appearance of the motives of modern epistemology. (shrink)
Intellectiva intuitio secundum Scotum: elementa doctrinaeProblema cognitionis individui qua talis, scil. quoad eius individualitatem („principii individuationis“) ad multas disceptationes ansam praebuit. In lumine revelationis Christianae quidem quaestio haec immo vehementius urget, nam fides Christiana primo singularia et individualia (et ideo contingentia) ante oculos ponit, universalia vero mere secundarie respicit. Ioannes Duns Scotus quaestionem hanc theologico-philosophicam tractans cognitionem intuitivam intellectivam totius rei individualis defendit, tria genera talis cognitionis distinguendo: primo cognitionem intuitivam intellectivam perfectam, quae non est possibilis nisi „in patria“, secundo (...) cognitionem intuitivam intellectivam directam sed imperfectam (scil. ad principium individuationis cognoscendum non penetrantem) quaeveritates contingentes actusque animae respicit, tertio cognitionem intuitivam intellectivam imperfectam et indirectam – actus commemorandi cognitiones intuitivas praeteritas. Ex his tribus intuitivae cognitionis modis, quomodo Scotus Aristotelis de cognitione doctrinam mutaverit, elucet.Intellective Intuition according to Scotus: the Basic ApproachThe problem of the intuition of the individual as such, i. e. of its individuality (the „principle of individuation“) gave rise to many controversies. The problem becomes especially urgent in the light of the Christian revelation, since Christianity in the first place relates to the singular and individual (and therefore contingent), whereas the universal assumes only a secondary rôle. John Duns Scotus deals with this theologico-philosophical problem and sets out to defend intellective intuition of the individual as a whole. He distinguishes three kinds within this type of cognition: perfect intuitive intellective cognition which is possible only in patria, direct but imperfect (i. e. not penetrating the principle of individuation) intuitiveintellective cognition which relates to contingent truths and spiritual acts, and, finally, imperfect and indirect intuitive intellective cognition, i. e. acts of recalling the past intuitive cognitions. In these three examples the fundamental Scotus’s arguments are exhibited and the extent to which Scotus transgresses the limits of Aristotelian epistemology is made clear. (shrink)
Bertrand Russell paid considerable attention to the problem of universals throughout his long life. One of main factors which contributed to Russell’s rejection of Hegelian philosophy (which is commonly viewed as a beginning of analytic philosophy) was rejection of so-called internal relations theory, according to which relations reduce to properties of relata or of the whole composed of them. For Russell relations were examples of indispensable universals. Russell is also famous for developing the similarity argument for realism: if we want (...) to get rid of universals by reducing them to sets of objects similar in a certain respect, we have to accept similarity as a genuine universal, for otherwise we are threatened by a vicious regress. The paper contains a presentation of evolution of Russell’s thought regarding universals and a defense of similarity argument against criticism of Michał Hempoliński, according to which causal explanations are sufficient to explain the similarity of objects. It is argued that such explanations are insufficient, as they do not apply to, for example, fundamental particles, like electrons, and the view that there are no fundamental (indivisible) particles is threatened by another vicious regress. (shrink)
The paper contains a comment on the criticism of the author's book Początek jest wszędzie (Prószynski i S-ka, 2002) by Marek Lagosz ("Przegląd Filozoficzny - Nowa Seria, 14, 2005, 121-133). The comment focuses on the following issues: (1) the conception of philosophy of physics; (2) some methodological questions, especially the role of models in physics; (3) some explanations concerning the model proposed by the present author and his coworkers. A few "ideological remarks" are also made.
